¿podemos dividir siempre que el denominador sea distinto de cero?

Answer:

9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.

[tex] \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} [/tex]

[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]

[tex] = \frac{3x + 2 - 2x + 3}{x + 5} [/tex]

[tex] \frac{x + 5}{x + 5} = 1[/tex]

10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.

[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]

[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]

The statement that is equivalent to each other would be =

2×(4+2)-6 = 14÷(3.5×2)+4. That is option A.

An equivalent equation is the type of equation that appears different but has the same answer when simplified or solved.

The first part;

=2×(4+2)-6

= 2×(6)-6

= 12-6 = 6

The second part;

= 14÷(3.5×2)+4

= 14÷7+4

= 2+4

= 6

Therefore, 2×(4+2)-6 = 14÷(3.5×2)+4. is a true statement.

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Answer:

50 meters/21.91 seconds = 2.282 m/sec

The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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The solution of the expression is 964.

To start solving this problem, let's find the sum of -29 and 303. The sum of two numbers is the result when you add them together. So,

-29 + 303 = 274

The sum of -29 and 303 is 274.

Now, let's find the sum of -52 and -638. To add two negative numbers, you just add their absolute values and put a negative sign in front of the result. So,

-52 + (-638) = -690

The sum of -52 and -638 is -690.

Finally, the problem asks us to subtract the sum of -52 and -638 from the sum of -29 and 303. To subtract one sum from another, we just subtract the second sum from the first. So,

( -29 + 303 ) - ( -52 + -638 )

We can simplify the expression by rearranging the terms:

274 - (-690)

When we subtract a negative number, it's the same as adding its absolute value. So,

274 + 690 = 964

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Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.

Three sides, three angles, plus three vertices make up a triangle.

Area of triangle  = 1/2*base *height

Area of unshaded portion = complete area - area of shaded triangle

Area of unshaded portion = 1/2*(20)*(8.1) - 1/2*8*(8.1)

Area of unshaded portion = 81 - 32.4

Area of unshaded portion = 48.6

Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.

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The rate of change of the area is 20π square inches per second.

The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:

A = πr^2 - πr'^2

where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.

To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:

dA/dt = d/dt (πr^2) - d/dt (πr'^2)

Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:

dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)

Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:

dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π

Therefore, the rate of change of the area is 20π square inches per second.

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Answer:

3(n + 6) = 2(n + 6) + (n + 6)

3(n + 6) = 3n + 18

Answer:

15 1/2

Step-by-step explanation:

hope this helped

The bearing of C from A is 90 degrees when B is equidistant from A and C.

In navigation and geometry, bearing refers to the direction or angle between two points, measured clockwise from a fixed reference direction. Typically, bearings are measured in degrees, with 0 degrees indicating a direction due north, 90 degrees indicating a direction due east, 180 degrees indicating a direction due south, and 270 degrees indicating a direction due west. Bearings can be expressed as either magnetic bearings or true bearings, depending on the reference direction used.

Let's assume that the distance from B to A and from B to C is the same.

To find the bearing of C from A, we can use the fact that the interior angles of a triangle sum up to 180 degrees. Therefore, we can first find the bearing of A from C:

180 - 129 = 51

This means that the bearing of C from A is 51 degrees in the opposite direction of the bearing of A from C. Since the bearing of A from C is 219, the bearing of C from A is:

219 - 180 + 51 = 90 degrees

Therefore, the bearing of C from A is 90 degrees.

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Answer:

0.000309 in scientific notation is 3.09 x 10^(-4)

Answer:

0.309x10 to the -4 power

Step-by-step explanation:

just move the decimal place back till its a whole number and do that number to the power of ten if that makes sense

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The area of the rugs in square yards with given dimensions 1/2 yard by 2 5/6 yards is equal to  1 5 /12 square yards.

Dimensions of the rug are,

1/2 yard by 2 5/6 yards

Area of the rug in square yards solved by Keith is equal to

=  1/2 times 2 5/6

= ( 1/ 2 ) × (  2 5/6 )

Convert mixed fraction into proper fraction we get,

2 5/6 = ( 6 × 2 + 5 ) / 6

⇒ 2 5/6 = 17 / 6

⇒ Area of the rug in square yards solved by Keith = ( 1 / 2 ) × ( 17 / 6 )

⇒ Area of the rug in square yards solved by Keith = ( 17 / 12 )

⇒ Area of the rug in square yards solved by Keith = 1 5 /12 square yards.

Therefore, the area of the rugs is equal to 1 5 /12 square yards.

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The probability regarding fewer than 30 people out of 250 people will consider working from home is 3.36%.

In order to calculate the probability for the given condition we need to perform binomial distribution

P(X < 30) = Σ P(X = x)

For x = 0 to 29

Here,

X = number of people from the sample who work from home

P = probability of an adult working from home

Given,

X = 250

P = 0.15

Now performing approximation to binomial distribution, leads to approximate X like a normal random variable with mean

Therefore,

μ = np

μ = 250 x 0.15

μ =  37.5

Now we have to evaluate the standard deviation

σ = √(np(1-p))

σ = √ 250 x 0.15 x (1 - 0.15)

σ ≈  4.08

Then we can proceed to standardized X

Z = (X - μ) / σ

P(X < 30) = P(Z < (30 - μ) / σ) = P(Z < (30 - 37.5) / 4.08)

≈ P(Z < -1.84)

Using standard distribution table

P(Z < -1.84) ≈ 0.0336

Converting it into percentage

0.0336 x 100

= 3.36%

The probability regarding fewer than 30 people out of 250 people will consider working from home is 3.36%.

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The theoretical probability of the spinner not landing on red is 0.875.

The total number of sections on the spinner is 8, out of which only one section is red. Therefore, the probability of the spinner landing on red is:

P(Red) = 1/8

The probability of the spinner not landing on red would be the probability of landing on any other section, which is:

P(Not Red) = 1 - P(Red) = 1 - 1/8 = 7/8

Therefore, the theoretical probability of the spinner not landing on red is 7/8 or 0.875 in decimal form.

So, the correct answer is: 0.875.

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Answer:

D

Step-by-step explanation:

Answer: The given inequality is:

y < c + 5

We can rewrite this inequality in slope-intercept form, y = mx + b, by isolating y:

y < c + 5

y - 5 < c

c > y - 5

In slope-intercept form, this is:

y = 1x + (-5)

The y-intercept of this boundary line is -5.

Step-by-step explanation:

The point of tangency is (-3, -2).

To find the point of  tangency , we really want to find the convergence point between the line and the circle. We can begin by tracking down the situation of the circle with focus (- 1,2).

A circle's equation for its center (a,b) and radius (r) is as follows:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Plugging in the values for the center and solving for r, we get:

[tex](x + 1)^2 + (y - 2)^2 = r^2[/tex]

Now we need to find the intersection point between this circle and the line 2x+3y=-22. We can do this by substituting y = (-2/3)x - (22/3) into the equation of the circle:

[tex](x + 1)^2 + ((-2/3)x - (16/3))^2 = r^2[/tex]

Expanding and simplifying, we get:

[tex]10x^2 + 24x + 44 = 9r^2[/tex]

Next, we can make use of the fact that the line intersects the circle at a tangent. This indicates that the distance between the intersection point and the center of the circle is the same as its radius. The distance between the center of the circle and the line can be determined using the distance formula:

distance = [tex]|2x + 3y - (-22)\sqrt{2^2 + 3^2}| = |2x + 3y + 22| \sqrt(13)[/tex]

Setting this equal to the radius r, we get:

[tex]|2x + 3y + 22| \sqrt{13} = \sqrt{10x^2 + 24x + 44} / 3[/tex]

Squaring both sides and simplifying, we get:

[tex]36(2x + 3y + 22)^2 = 13(10x^2 + 24x + 44)[/tex]

Expanding and simplifying, we get:

[tex]26x^2 + 36xy + 45y^2 + 52x + 132y + 240 = 0[/tex]

Now we can use the quadratic formula to solve for x:

x = (-18y - 13 ± [tex]\sqrt{169 - 720y^2[/tex])) / 13

Substituting this into the equation for the line, we get:

2(-18y - 13 ± [tex]\sqrt{169 - 720y^2))[/tex] / 13 + 3y = -22

Simplifying, we get:

y = -2

Substituting y = -2 into the equation for x, we get:

x = -3

Therefore, the point of tangency is (-3, -2).

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Answer: 64 sqaure centimetres.

Step-by-step explanation:

- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.

Top and Bottom

4 x 4 = 16

16 x 2 = 32

Both faces are the same so once we find the area of one, we can just double it.

North, South, East and West Side

4 x 2 = 8

8 x 4 = 32

All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.

To find the overall surface area add all the areas you have.

32 + 32 = 64

or

16 +_16 + 8 + 8 + 8 + 8 = 64

Answer: y=1/2x-3

Step-by-step explanation:

I'm assuming you're trying to find it in slope intercept form!

y=mx+b

y=1/2x-3

easy

Answer:

f(x + 1) + 2

Step-by-step explanation:

All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.

P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.

The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.

In the triangle HIJ,

The measure of angle J is equal to 90 degrees.

This implies ,

HI is the hypotenuse.

JH is the opposite side to angle I.

In triangle HIJ,

Using trigonometric ratio we get,

sin ∠I = Opposite side / Hypotenuse

Substitute the values we have,

⇒ sin ∠I = 4.8 / 6.7

⇒ sin ∠I = 0.72

Now , take sin⁻¹ both the side of the equation we get,

⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )

Here sin⁻¹(sin ∠I) = ∠I

⇒∠I = sin⁻¹( 0.72 )

⇒∠I = 46.05 degrees

Therefore, the measure of angle I is equal to 46.05 degrees.

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The game owner should charge option (a) $0.55 to make it a fair game

To determine how much the game owner should charge to make it a fair game, we need to calculate the average value of each package. We can do this by finding the total value of all the packages and dividing it by the total number of packages.

The total value of the 30 packages worth $.65 each is:

30 x $.65 = $19.50

The total value of the 10 packages worth $.60 each is:

10 x $.60 = $6.00

The total value of the 15 packages worth $.30 each is:

15 x $.30 = $4.50

The total value of all the packages is

$19.50 + $6.00 + $4.50 = $30.00

The total number of packages is

30 + 10 + 15 = 55

The average value of each package is

$30.00 / 55 = $0.55

Therefore, the correct option is (a) $0.55

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Answer:

Step-by-step explanation:

If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.

what is deposit ?

In the context of finance, a "deposit" refers to the act of placing money or funds into a bank account, investment account, or other financial account. A deposit can also refer to the initial payment made to secure or initiate a purchase

In the given question,

To calculate the sinking fund payment that Mary needs to make at the end of each quarter, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)ⁿᵇ - 1]/(r/n)

Where:

FV = future value (the amount Mary needs to accumulate, which is $9,000 in this case)

PMT = payment per period (what Mary needs to find)

r = annual interest rate (4% in this case)

n = number of compounding periods per year (4, since interest is compounded quarterly)

t = number of years (9 in this case)

Substituting these values into the formula, we get:

$9,000 = PMT x [(1 + 0.04/4)³⁶ - 1]/(0.04/4)

Simplifying and solving for PMT, we get:

PMT = $9,000 / [(1.01³⁶ - 1)/0.01]

PMT = $9,000 / 31.8422

PMT = $282.44 (rounded to the nearest cent)

Therefore, Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.

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Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.

1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).

Step 1: Set up the equation using the given information.

One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:

Reciprocal of the original number + 1 = $\frac{7}{3}$

Step 2: Solve for the reciprocal of the original number.

Reciprocal of the original number = $\frac{7}{3}$ - 1

Step 3: Simplify the equation.

Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$

Reciprocal of the original number = $\frac{4}{3}$

Step 4: Find the original number.

Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:

Original number = $\frac{1}{(\frac{4}{3})}$

Step 5: Simplify the expression.

Original number = $\frac{1}{1} \times \frac{3}{4}$

Original number = $\frac{3}{4}$

The original number expressed as a common fraction is $\frac{3}{4}$.

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Answer:

(z - 1) (z + 19)

Step-by-step explanation:

z² + 18z - 19

Consider the form x² + bx + c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is −19 and whose sum is 18.

-1, 19

Write the factored form using these integers.

(z - 1) (z + 19)

If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.

Explain month

A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.

According to the given information

If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:

$2299.99 * (1 + 0.020825)²⁴ = $3,637.16

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Step-by-step explanation:

Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3